Numerical simulation of cavitating flow using the upstream finite element method

A finite element method is proposed to predict cavitating flows in arbitrarily shaped channels. An upwind scheme, based on the Petrov-Galerkin method using an exponential weighting function, is employed to eliminate the numerical instability due to the advection term. The solution algorithm is parallel to a fractional step method. The calculation domain is divided into quadrilateral elements. The pressure is defined at the centroid of the element and assumed to be constant within the element. The other variables, such as the velocity and void fraction, are defined on the nodes. Cavitating flows around a circular cylinder are simulated by the present finite element method. The cavitation occurrence relates closely to the vortex motion of the water in the sheared layer in accordance with experimental observations, and the cavitation regions almost coincide with the regions where cavitation bubbles are observed frequently in experiments. This indicates that the present method is indeed applicable to the prediction of cavitating flows. (C) 1998 Elsevier Science Inc. All rights reserved.